InterviewSolution
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InterviewSolution
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Tangent is drawn at the point `(x_i ,y_i)`on thecurve `y=f(x),`whichintersects the x-axis at `(x_(i+1),0)`. Now, again a tangent is drawn at `(x_(i+1,)y_(i+1))`on thecurve which intersect the x-axis at `(x_(i+2,)0)`and theprocess is repeated `n`times, i.e.`i=1,2,3dot,ndot`If `x_1,x_2,x_3,ddot,x_n`from anarithmetic progression with common difference equal to `(log)_2e`and curvepasses through `(0,2)dot`Now ifcurve passes through the point `(-2, k),`then thevalue of `k`is____ |
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Answer» Correct Answer - 8 Equation of tangent at `P(x_(1),y_(1))` of `y=f(x)` is `y-y_(1) =(dy)/(dx)(x-x_(1))` This tangent cuts the x-axis. So, `x_(2)=x_(1)-y_(1)/((dy)/(dx))` `x_(1),x_(2),x_(3),………..,x-(n)` are in A.P. `x_(2)-x_(1)=-y_(1)/((dy)/(dx))=log_(2)e` (Given) or `-y=log_(2)e(dy)/(dx)` or `(dy)/ylog_(2)e=-dx` Integrating both sides, we get `log_(e)y=-xloge^(2)+c` Since `y=f(x)` passes through (0,2), `k=2` `therefore y=2.e^(-xlog_(e)2)` `therefore y=e^(1-x)` |
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